Systems modeling based on Legendre polynomials

A new method for obtaining models of continuous systems, based on Legendre orthogonal filters, is proposed in this paper. Recent results in the field of orthogonal functions were used to improve accuracy of modeling. First, Legendre orthogonal filters were designed on the basis of orthogonal functions. Then, adjustable models were formed. Models parameters were optimized using genetic algorithm. As a case study, an experimental simple DC drive was considered and described in details. Simulations were performed out to approve theoretical results and demonstrate that the method described in the paper is very suitable for modeling continuous systems. It achieves excellent results in the sense of model accuracy and modeling algorithm speed.